Pressure balance inconsistency exhibited in a statistical model of magnetospheric plasma

While quantitative theories of plasma flow from the magnetotail to the inner magnetosphere typically assume adiabatic convection, it has long been understood that these convection models tend to overestimate the plasma pressure in the inner magnetosphere. This phenomenon is called the pressure crisis or the pressure balance inconsistency. In order to analyze it in a new and more detailed manner we utilize an empirical model of the proton and electron distribution functions in the near‐Earth plasma sheet (−50RE<X< −10RE), which uses the Tsyganenko[1989] magnetic field model and a plasma sheet representation based upon several previously published statistical studies. We compare our results to a statistically derived particle distribution function at geosynchronous orbit. In this analysis the particle distribution function is characterized by the isotropic energy invariant λ =EV2/3, whereEis the particle's kinetic energy andVis the magnetic flux tube volume. The energy invariant is conserved in guiding center drift under the assumption of strong, elastic pitch angle scattering. If, in addition, loss is negligible, the phase space densityf(λ) is also conserved along the same path. The statistical model indicates thatf(λ, ) is approximately independent ofXforX≤ −35REbut decreases with increasingXforX≥ −35RE. The tailward gradient off(λ, ) might be attributed to gradient/curvature drift for large isotropic energy invariants but not for small invariants. The tailward gradient of the distribution function indicates a violation of the adiabatic drift condition in the plasma sheet. It also confirms the existence of a “number crisis” in addition to the pressure crisis. In addition, plasma sheet pressure gradients, when crossed with the gradient of flux tube volume computed from the Tsyganenko[1989] magnetic field model, indicate Region 1 currents on the dawn and dusk sides of the outer plasma sheet.